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What is a Lock-In Amplifier?

A lock-in amplifier is a type of amplifier used to extract quiet signals out of noisy data. High quality lock-in amplifiers can extract signals up to a million times quieter than the surrounding noise. The output of a lock-in amplifier is a DC signal showing the strength of the signal to be extracted.

How Does a Lock-In Amplifier Work?

Conceptually, a lock-in amplifier works by exploiting the orthogonality of sinusoidal functions. Use of a lock-in amplifier requires a clear reference signal at the frequency of the signal to be extracted. This reference signal is multiplied by the noisy input signal and the product is integrated over a set time. When sinusoidal functions are multiplied together and integrated over a significant amount of time, the result will be zero unless the two sinusoidal functions have the same frequency. This is the before-mentioned orthogonality of sinusoidal functions. For the output of a lock-in, this means that the contributions of all signals not at the reference frequency will be attenuated very close to zero. The output is a DC signal showing the strength of the original input signal at the reference frequency.

From a circuits standpoint, a lock-in amplifier consists of a homodyne detector followed by an adjustable low pass filter. Traditional lock-in amplifiers used analog frequency mixers and RC filters for the demodulation, but modern devices are typically digital and use fast digital signal processing. The out of phase component of the signal that has the same frequency as the reference signal is also attenuated (sine functions are orthogonal to cosine functions of the same frequency), making lock-in amplifiers phase sensitive detectors. Sine and cosine demodulation is usually performed simultaneously (dual phase demodulation).

Try it in the Lab

There are multiple lock-in amplifiers in the lab, so the choice of which to use is yours. There is one Model 5104 from Princeton Applied Research that may not be working properly, so you may want to avoid that device. The Model 5202 from Princeton Applied Research was tested and seems to be working as it should. Each lock-in amplifier has slightly different menus/controls, but the basics are all similar.

Now that we have our equipment and a space in the lab to work we can set up our instruments. All devices must of course be powered but for now the lock-in doesn't have to be connected to the function generator. The lock-in's output should be connected to the oscilloscope though. Hopefully the function generator that you're using has two outputs, if it doesn't then another function generator might have to be used. One of these outputs will be the reference signal and the other will be the lock-in's input signal. Both signals should be sine waves for now and the frequencies of each can be set to whatever you desire, but if you're using the Model 5202 for example, then there is a corresponding setting on the lock-in for the reference signal frequency. So you should make sure that dial is set to the right setting for whatever reference frequency you're using. Something like 1 MHz should work.

The amplitudes of each signal are once again up to you, but the Model 5202 lock-in has a maximum input voltage of 5 Vrms, so make sure the amplitude of that signal is below that. Something like 5 mVpp should work. The reference signal on the other hand should be slightly larger. Something like 1 Vpp, for example.

There are various settings on the front of the lock-in, some of which should be looked at. The first dial on the left (Model 5202) represents a sensitivity, and for now can be set to something like 25 mV. This can be changed later to make our equipment more sensitive. There is also a setting for the reference phase (0 deg, 90 deg, 180 deg, etc.). This is the phase difference applied to the reference signal when compared to the input signal. For now it can be left to 0 degrees. There may also be a setting for what waveform the reference will be. We would want that set to a standard sinusoidal waveform. The Model 5202 has some other Output settings as well, most of which can be left at the default. The time constant can be left at the lowest value (ex. 10 ms).

Hopefully the "Unlock" light on the lock-in amplifier (if it has one) is currently lit up, signifying that there is no reference signal locked. Now we should plug in our reference output from the function generator into the reference input of the lock-in. After plugging in the BNC and making sure that the function generator output is active we should see the "Unlock" light turn off. That means the lock-in is locked to the reference frequency. Now we can plug in our input signal from the function generator to the lock-in. After doing so we should see an output voltage showing up on the oscilloscope (and also on the front of the Model 5202). The lock-in amplifier is now locked in on the reference frequency and displaying the strength of that signal. If you change the signal strength of the input signal then you should see the output change accordingly. If you change the frequency of the reference or input signals the output of the lock-in should drop off as well.

The Model 5202 is an advanced lock-in amplifier and it has two outputs, one labeled 'in-phase' and the other labeled 'quadrature'. This lock-in actually does the entire calculation twice, the second time with a 90 degree phase shift between input and reference. These two output quantities represent the signal as a vector relative to the lock-in reference oscillator. By computing the magnitude of the signal vector (adding the 'in-phase' and 'quadrature' values in quadrature), the phase dependency is removed.

So far the results of our lock-in amplifier are less than exciting. We are inputting a sine wave and the lock-in tells us its strength. The real use of a lock-in is of course to pull a quiet signal out of a noisy environment.

Simplified Circuit

Lock-in amplifiers are important and powerful devices, but their circuits are not particularly complicated. The block diagram consists of five parts and is shown below:

1. AC amplifier, called the signal amplifier;

2. Voltage controlled oscillator (VCO);

3. Multiplier, called the phase sensitive detector (PSD);

4. Low-pass filter; and

5. DC amplifier.

The AC amplifier is simply a voltage amplifier combined with variable filters. Some
lock-in amplifiers let you change the filters as you wish, others do not. Some lock-in
amplifiers have the output of the AC amplifier stage available at the signal monitor
output. Many do not.

The voltage controlled oscillator is just an oscillator, except that it can synchronize with
an external reference signal (i.e., trigger) both in phase and frequency. Some lock-in
amplifiers contain a complete oscillator and need no external reference. In this case they
operate at the frequency and amplitude that you set, and you must use their oscillator
output in your experiment to derive the signal that you ultimately wish to measure.
Virtually all lock-in amplifiers are able to synchronize with an external reference signal.
The VCO also contains a phase-shifting circuit that allows the user to shift its signal from
0-360 degrees with respect to the reference.

The phase sensitive detector is a circuit which takes in two voltages as inputs V1 and V2
and produces an output which is the product V1*V2. That is, the PSD is just a multiplier
circuit.

The low pass filter is an RC filter whose time constant may be selected. In many cases
you may choose to have one RC filter stage (single pole filter) or two RC filter stages in
series (2-pole filter). In newer lock-in amplifiers, this might be a digital filter with the
attenuation of a "many pole" filter.

The DC amplifier is just a low-frequency amplifier similar to those frequently assembled
with op-amps. It differs from the AC amplifier in that it works all the way down to zero
frequency (DC) and is not intended to work well at very high frequencies, say above 10
KHz.